# cvode: cvode In sundialr: An Interface to 'SUNDIALS' Ordinary Differential Equation (ODE) Solvers

## Description

CVODE solver to solve stiff ODEs

## Usage

 ```1 2 3 4 5 6 7 8``` ```cvode( time_vector, IC, input_function, Parameters, reltolerance = 1e-04, abstolerance = 1e-04 ) ```

## Arguments

 `time_vector` time vector `IC` Initial Conditions `input_function` Right Hand Side function of ODEs `Parameters` Parameters input to ODEs `reltolerance` Relative Tolerance (a scalar, default value = 1e-04) `abstolerance` Absolute Tolerance (a scalar or vector with length equal to ydot, default = 1e-04)

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56``` ```# Example of solving a set of ODEs with cvode function # ODEs described by an R function ODE_R <- function(t, y, p){ # vector containing the right hand side gradients ydot = vector(mode = "numeric", length = length(y)) # R indices start from 1 ydot[1] = -p[1]*y[1] + p[2]*y[2]*y[3] ydot[2] = p[1]*y[1] - p[2]*y[2]*y[3] - p[3]*y[2]*y[2] ydot[3] = p[3]*y[2]*y[2] # ydot[1] = -0.04 * y[1] + 10000 * y[2] * y[3] # ydot[3] = 30000000 * y[2] * y[2] # ydot[2] = -ydot[1] - ydot[3] ydot } # ODEs can also be described using Rcpp Rcpp::sourceCpp(code = ' #include using namespace Rcpp; // ODE functions defined using Rcpp // [[Rcpp::export]] NumericVector ODE_Rcpp (double t, NumericVector y, NumericVector p){ // Initialize ydot filled with zeros NumericVector ydot(y.length()); ydot[0] = -p[0]*y[0] + p[1]*y[1]*y[2]; ydot[1] = p[0]*y[0] - p[1]*y[1]*y[2] - p[2]*y[1]*y[1]; ydot[2] = p[2]*y[1]*y[1]; return ydot; }') # R code to genrate time vector, IC and solve the equations time_vec <- c(0.0, 0.4, 4.0, 40.0, 4E2, 4E3, 4E4, 4E5, 4E6, 4E7, 4E8, 4E9, 4E10) IC <- c(1,0,0) params <- c(0.04, 10000, 30000000) reltol <- 1e-04 abstol <- c(1e-8,1e-14,1e-6) ## Solving the ODEs using cvode function df1 <- cvode(time_vec, IC, ODE_R , params, reltol, abstol) ## using R df2 <- cvode(time_vec, IC, ODE_Rcpp , params, reltol, abstol) ## using Rcpp ## Check that both solutions are identical # identical(df1, df2) ```

sundialr documentation built on May 16, 2021, 5:06 p.m.